We give an improved upper bound for the error term in the Riemann-von Mangoldt formula for functions of degree 0 in the extended Selberg class. The bound is uniform for functions with no zeros in a certain half-plane. The first such bound was given by J. Kaczorowski and A. Pereili  in the proof that the extended Selberg class is a semigroup with factorization.
Maciej Radziejewski. "On the zeros of functions from the extended Selberg class of degree 0." Funct. Approx. Comment. Math. 33 97 - 100, 2005. https://doi.org/10.7169/facm/1538186604